Elliptic and parabolic equations for measures

Vladimir I. Bogachev; Nikolai V. Krylov; Michael Röckner

doi:10.1070/RM2009v064n06ABEH004652

Elliptic and parabolic equations for measures

Vladimir I. Bogachev, Nikolai V. Krylov, Michael Röckner

Mathematics

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58 Scopus citations

Abstract

This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L^p-spaces with respect to infinitesimally invariant measures are investigated.

Original language	English (US)
Pages (from-to)	973-1078
Number of pages	106
Journal	Russian Mathematical Surveys
Volume	64
Issue number	6
DOIs	https://doi.org/10.1070/RM2009v064n06ABEH004652
State	Published - 2009

Keywords

Elliptic equation
Parabolic equation
Stationary distribution of a diffusion process
Transition probability

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title = "Elliptic and parabolic equations for measures",

abstract = "This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in Lp-spaces with respect to infinitesimally invariant measures are investigated.",

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T1 - Elliptic and parabolic equations for measures

AU - Bogachev, Vladimir I.

AU - Krylov, Nikolai V.

AU - Röckner, Michael

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AB - This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in Lp-spaces with respect to infinitesimally invariant measures are investigated.

KW - Elliptic equation

KW - Parabolic equation

KW - Stationary distribution of a diffusion process

KW - Transition probability

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ER -

Elliptic and parabolic equations for measures

Abstract

Keywords

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